THE STRESS STATE OF THE RADIALLY INHOMOGENEOUS HEMISPHERICAL SHELL UNDER LOCALLY DISTRIBUTED VERTICAL LOAD

Vestnik MGSU 12/2017 Volume 12
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, Head of the Resistance of Materials Department, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Kapliy Daniil Aleksandrovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Postgraduate student, Resistance of Materials Department, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 1326-1332

Subject: one of the promising trends in the development of structural mechanics is the development of methods for solving problems in the theory of elasticity for bodies with continuous inhomogeneity of any deformation characteristics: these methods make it possible to use the strength of the material most fully. In this paper, we consider the two-dimensional problem for the case when a vertical, locally distributed load acts on the hemisphere and the inhomogeneity is caused by the influence of the temperature field. Research objectives: derive governing system of equations in spherical coordinates for determination of the stress state of the radially inhomogeneous hemispherical shell under locally distributed vertical load. Materials and methods: as a mechanical model, we chose a thick-walled reinforced concrete shell (hemisphere) with inner and outer radii a and b, respectively, b > a. The shell’s parameters are a = 3.3 m, b = 4.5 m, Poisson’s ratio ν = 0.16; the load parameters are f = 10MPa - vertical localized load distributed over the outer face, θ0 = 30°, temperature on the internal surface of the shell Ta = 500 °C, temperature on the external surface of the shell Tb = 0 °C. The resulting boundary-value problem (a system of differential equations with variable coefficients) is solved using the Maple software package. Results: maximal compressive stresses σr with allowance for material inhomogeneity are reduced by 10 % compared with the case when the inhomogeneity is ignored. But it is not so important compared with a 3-fold decrease in the tensile stress σθ on the inner surface and a 2-fold reduction in the tensile stress σθ on the outer surface of the hemisphere as concretes generally have a tensile strength substantially smaller than the compressive strength. Conclusions: the method presented in this article makes it possible to reduce the deformation characteristics of the material, i.e. it leads to a reduction in stresses, which allows us to reduce the thickness of the reinforced concrete shell, and also more rationally distribute the reinforcement across the cross-section, increase the maximum values of the mechanical loads.

DOI: 10.22227/1997-0935.2017.12. 1326-1332

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Using topological transformations of the sphereto design surfaces having two families of light lines

Vestnik MGSU 9/2013
  • Teplyakov Aleksandr Avramovich - Moscow State University of Civil Engineering (MGSU) Associate Professor, Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Vavanov Dmitriy Alekseevich - Moscow State University of Civil Engineering (MGSU) Senior Lecturer, Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 149-152

He authors discuss construction of surfaces having two families of light lines using topological transformations of the sphere. The light framework of surfaces, meeting esthetic requirements, is designed in various ways, which can be reduced to the design of a framework of proportional and congruent curves. Topological transformation of the sphere into a surface of the same topological class is considered as a method for design of continuous surfaces having two families of light lines. Transformation of points of the constructed surface is performed together with the space of three mutually perpendicular beam planes, as well as beams of radial planes. This method, employed for the construction of the frame surface and light lines, may be used to generate aesthetically attractive surfaces. The shape of the contour surface can be varied within certain limits, although it maintains its pre-set parameters.

DOI: 10.22227/1997-0935.2013.9.149-152

References
  1. Polezhaev Yu.O., Borisova A.Yu. Lineynye variatsii modelirovaniya svoystv elliptichnosti [Modeling the Properties of Ellipticity: Linear Variations]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 8, pp. 34—38.
  2. Gil'bert D. Osnovaniya geometrii [Fundamentals of Geometry]. Available at: http://ilib.mccme.ru/djvu/geometry/osn_geom.htm. Date of access: 2.11.2012.
  3. Alexander S., Ghomi M. The Convex Hull Property and Topology of Hypersurfaces with Nonnegative Curvature. Adv. Math. 2003, p. 327.
  4. Gil'bert D., Kon-Fossen S. Naglyadnaya geometriya [Visual Geometry]. Moscow, 2010, p. 102.
  5. Peklich V.A. Mnimaya nachertatel'naya geometriya [Imaginary Descriptive Geometry]. Moscow, 2007, p. 114.
  6. Alexander S., Ghomi M. The Convex Hull Property of Noncompact Hypersurfaces with Positive Curvature. Amer. J. Math. 2004, p. 216.
  7. Ekholm T. Regular Homotopy and Total Curvature. I. Circle Immersions into Surfaces. Algebr. Geom. Topol. 2006, p. 461. Available at: http://www.maths.tcd.ie/EMIS/journals/AGT/ftp/main/2006/agt-06-16.pdf. Date of access: 26.06.2013.
  8. Ekholm T. Regular Homotopy and Total Curvature. II. Sphere Immersions into 3-space. Algebr. Geom. Topol. 2006, p. 493. Available at: http://www.maths.tcd.ie/EMIS/journals/AGT/ftp/main/2006/agt-06-17.pdf. Date of access: 26.06.2013.
  9. Sobolev N.A. Obshchaya teoriya izobrazheniy [General Theory of Images]. Moscow, 2004, p. 173.
  10. Eliashberg Y., Mishachev N. Introduction to the h-principle. Graduate Studies in Mathematics. Providence, RI. 2002, vol. 48, p. 247.

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